Inter-Node Distance Estimation fromMultipath Delay Differencesof Channels to Observer NodesGregor Dumphart, Marc Kuhn, Armin Wittneben, Florian Trösch

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 1 / 16

Wireless Distance Estimation: State of the Art

Standard Approach:Compute distance estimated̂ given CIR h(τ)

Node B

Node A

d

h(τ)

Received Signal Strength– Poor accuracy (fluctuations)

Round-Trip Time of Arrival– Complex hardware at both ends– Large relative error at short distance– Requires line of sight

(indirectly)

Time Difference of Arrival– Requires precise anchor sync.– Requires line of sight

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 2 / 16

Wireless Distance Estimation: Proposed Paradigm

Idea: Compute a distance estimate d̂ by comparing thewideband CIRs hA(τ) and hB(τ) to an observer node.

• Can this idea be realized? How to estimate d ?

• Does the concept offer advantages to wireless localization?

Node B

Node AObserver

d

hA(τ)

hB(τ)

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 3 / 16

Outline

Distance Estimation from Multipath Delays: Basic Principle

Estimation-Theoretic Properties

Performance in Realistic Conditions

Technological Advantages & Opportunities

Summary & Outlook

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 4 / 16

Channel Impulse Response:Shifts due to Local Displacement

Explanation videos are hosted at:

https://www.nari.ee.ethz.ch/wireless/research/

downloads/ICC2019ConceptVideo.mp4

https://www.nari.ee.ethz.ch/wireless/research/

downloads/ICC2019ConceptVideoDelayDiff.mp4

https://www.nari.ee.ethz.ch/wireless/research/

downloads/ICC2019ConceptVideoExtended.mp4

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 5 / 16

Channel Impulse Response:Shifts due to Local Displacement (Video Backup)

0 2 4 6 8 10 12

x [m]

0

2

4

6

8

y [m

]

Observer

Node A

Node B

20 30 40 50 60 70

[ns]

|h(

)|

CIR between Observer and Node ACIR between Observer and Node B

0 2 4 6 8 10 12

x [m]

0

2

4

6

8

y [m

]

Observer

Node A

Node B

20 30 40 50 60 70

[ns]

|h(

)|

CIR between Observer and Node ACIR between Observer and Node B

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 6 / 16

Distance Estimation from Multipath Delays:Basic PrincipleMultipath components k = 1 . . .K extracted from bothhA(τ) and hB(τ). Directions of arrival/departure are unknown.We consider the delay differences

∆k = τB,k − τA,k .

Propagation at speed of light c inflicts the bound

d ≥ c · |∆k| ∀k = 1 . . .K .

For rich multipath from diverse directions, the largest c · |∆k| willbe close to d. This yields an estimation rule (synchronous case)

d ≈ c ·maxk|∆k| .

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 7 / 16

Distance Estimation from Multipath Delays:Asynchronous CaseWithout precise synchronization, the delay differences

∆̃k = ∆k + ε

are observed subject to an unknown clock offset ε.

The ∆̃k are bounded by−d+ cε ≤ c∆̃k ≤ d+ cε

and thus, for rich multipath,

d+ cε ≈ c ·maxk

∆̃k

−d+ cε ≈ c ·mink

∆̃k

Addition and subtraction yieldestimation rules (async. case)

d ≈ c

2

(maxk

∆̃k −mink

∆̃k

)ε ≈ 1

2

(maxk

∆̃k + mink

∆̃k

)G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 8 / 16

Estimation-Theoretic PropertiesEmployed assumptions:

1. MPC directions have i.i.d. uniform distribution in 3D

2. Delays τA,k and τB,k can be associated

3. Delays τA,k and τB,k were extracted without error

Synchronous AsynchronousMaximum-LikelihoodEstimate

d̂ML =

c ·maxk|∆k|d̂ML =c2

(maxk∆̃k −mink∆̃k

)Bias-Corrected(UMVUE)

d̂ = K+1K d̂ML d̂ = K+1

K−1 d̂ML

RMSE of d̂ ≈ d/K ≈√

2 · d/K

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 9 / 16

Distance Estimation for Noisy Delay Extraction

Consider delay differences Tk = ∆k + nk observed with error nk.Estimates that account for the error statistics are given by

Sync. case: d̂ML ∈ arg maxd

1

dK

K∏k=1

Ik(Tk, d)

Async. case:(d̂ML, ε̂ML

)∈ arg max

d,ε

1

dK

K∏k=1

Ik(T̃k − ε, d)

where Ik(Tk, d) = Fnk(Tk + d

c )− Fnk(Tk − d

c ) is a soft version ofindicator function 1[− d

c, dc](Tk) and Fnk

is the CDF of nk.

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 10 / 16

Performance in Realistic Conditions:Ray-Tracing Study in an Indoor Environment

0 2 4 6 8 10

0

1

2

3

4

-1

-0.5

0

0.5

1

x [m]

y[m

]

node A (static)

observernode

dis

tan

cees

t.er

ror[m

]

(a) Asynchronous case

-1

-0.5

0

0.5

1

dis

tan

cees

t.er

ror[m

]

node A (static)

observernode 1

observernode 2

observernode 3

(b) Asynchronous case, three observers

• Reflections at walls, floor, ceiling

• MPC detection criterion considersdiffuse multipath and AWGNfor 1GHz bandwidth

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

Errorless extracted delays, using UMVUEGaussian errros at B = 1 GHz, using MLE

synchronous

asynchronous

distance d [m]

dist

ance

RM

SE[m

]

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 11 / 16

Technological Advantages of the Scheme

• Adding observers is trouble-free and improves accuracy

• Does not require line of sight• Does not require precise time synchronization . . .

. . . between node A and B (although it helps)

. . . between an observer and node A or B

. . . between observers

• Does not require knowledge of propagation environment• Does not require knowledge of observer location

−→ mobiles can be observers!

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 12 / 16

Application & Opportunities 1

Distance estimate tolow-power transmit-onlybeacon→ ranging orregioning (fingerprintingwith live re-calibration)

fixed beacon(transmit only)

mobile

Distance estimates tomultiple beacons→ estimate mobileposition (trilateration)

fixed beacons

mobile

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 13 / 16

Application & Opportunities 2

Conventional wirelesslocalization: trilaterationwith d-estimatesto anchors

mobile

mobile

anchor 1 anchor 2

anchor 3

Our scheme offers a novelway for inter-mobiledistance estimation inan anchor setup, e.g. forcooperative localization

mobile

anchor 1 asobserver

anchor 2 asobserver

anchor 3 asobserver

mobile

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 14 / 16

Application & Opportunities 3

Wireless networkwith unknownarrangement

Each mobile canserve as observer!

1.)

2.)

3.)

. . . (repeat for all pairs)

Use inter-user destimates to computenetwork arrangement(cooperative networklocalization)

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 15 / 16

Summary & Outlook

• We proposed a novel paradigm for distance estimationbetween two wireless nodes by comparing their CIRs to anobserver node.

• We derived distance estimates from multipath delay shifts . . .. . . with/without precise time synchronization. . . with/without errors on the extracted delays

• The scheme offers great advantages and opportunities towireless indoor localization.

• [open] Performance in practice?

• [open] Impact of MPC association problem?

• [open] Other ways to realize the paradigm?

G. Dumphart, Distance Estimation from Multipath Delays IEEE ICC 2019 16 / 16